Why is symmetry not working in Texture Paint with my posed character?
After trial and error I discovered that by turning off visibility in the armature modifier, the symmetry goes back to working. This taught me that the painting symmetry is based on the global coordinates and original position, not the pose it happens to be in. 
If using Texture Paint with symmetry, toggle the visibility of the armature modifier off for the session unless the misalignment is intentional.